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L7 All Kind of Patterns in Recursion

In this Lecture we learn all about the Different-Different pattern based on Recursion In the prevesely lecture we know in depth all about the Subsecquance in depth

P1 Print All the Subsequence whos Sum is Equal to the K

in this Problem our task is print all the Subsecquance that sum is == to the k or given Sum

Example 1:
Input: nums = [1,2,1],Sum = 2
Output: [1,1],[2]

Again we used the concept of the Pick and Not Pick and check is Sum fo the subsecquance is equal to the given k store that particular subsecquance in the DS.

Sudo Code

Recursion Tree

Notes

Note: Zoom for Better Understanding

Code Zone!

Time Complexity:O(2 ^ N) For every Iteration we have tuple of option take or not take Exponintial Time
Space Complexity:O(N)+O(N) O(N) for the Recursive Stack Space and O(N) for Store the our element that is our Subsecquances.

P2 Print Only One Subsequence whos Sum is Equal to the K

This is the Modifiyed problem of the Preveous One in this Problem our task is only find the Single Subsequence and Stop the Iteration.

Sudo Code

Code Zone!

Time Complexity:O(2 ^ N) For every Iteration we have tuple of option take or not take Exponintial Time
Space Complexity:O(N)+O(N) O(N) for the Recursive Stack Space and O(N) for Store the our element that is our Subsecquances.

P3 Total Count the Subsequence whos Sum is Equal to the K

This is Agian the Modifiyed problem of the Preveous One in this Problem our task is only count the Number of the Subsecquance that Sum is == K

Again we used the concept of the Pick and Not Pick and check is Sum fo the subsecquance is equal to the given k

Preversely We Maintain the Array for count the Element that Sum is Equal to the k and that array print it.

But here we used at the Palced of the Array used a Variable for Cout the Subsecquance

Sudo Code

Recursion Tree
Complete Tree in the Notes

Code Zone!

Time Complexity:O(2 ^ N) For every Iteration we have tuple of option take or not take Exponintial Time
Space Complexity:O(N) O(N) for the Recursive Stack Space.